Does this mean that Avatar will be pulled from theatres before April 22? I think (though maybe I'm wrong) that movies tend to leave theatres before their home video release.

It is likely.

Avatar is pulled from roughly 100 movie theaters a week in the US with weekly world-wide ticket sales of roughly $20-30m, while decreasing about 15% a week. By the time April 22 comes around, it is likely Avatar will be out of most RealD and 2D theaters (IMAX is a different story however, as it continues to be sold out from repeat watchers), setting it up rather well for a re-release...